Corner Transfer Matrix Renormalization Group Method Applied to the Ising Model on the Hyperbolic Plane

Critical behavior of the Ising model is investigated at the center of large scale finite size systems, where the lattice is represented as the tiling of pentagons. The system is on the hyperbolic plane, and the recursive structure of the lattice makes it possible to apply the corner transfer matrix renormalization group method. From the calculated nearest neighbor spin correlation function and the spontaneous magnetization, it is concluded that the phase transition of this model is mean-field like. One parameter deformation of the corner Hamiltonian on the hyperbolic plane is discussed.Comment: 4 pages, 5 figure

Filling-dependence of the zigzag Hubbard ladder for a quasi-one-dimensional superconductor Pr_2Ba_4Cu_7O_{15-delta}

We investigate filling dependence of the zigzag Hubbard ladder, using density matrix renormalization group method. We illustrate the chemical-potential vs. electron-density and spin gap vs. electron density curves, which reflect characteristic properties of the electron state.On the basis of the obtained phase diagram, we discuss the connection to a novel quasi-one-dimensional superconductor Pr$_2$Ba$_4$Cu$_7$O$_{15-\delta}$.Comment: 5 pages, 6 figures, fig.4 is adde

Fractional S^z excitation and its bound state around the 1/3 plateau of the S=1/2 Ising-like zigzag XXZ chain

We present the microscopic view for the excitations around the 1/3 plateau state of the Ising-like zigzag XXZ chain. We analyze the low-energy excitations around the plateau with the degenerating perturbation theory from the Ising limit, combined with the Bethe-form wave function. We then find that the domain-wall particles carrying $S^z=\pm 1/3$ and its bound state of $S^z=\pm 2/3$ describe well the low-energy excitations around the 1/3 plateau state. The formation of the bound state of the domain-walls clearly provides the microscopic mechanism of the cusp singularities and the even-odd behavior in the magnetization curve.Comment: 13 pages, 15 figure

On calculation of vector spin chirality for zigzag spin chains

We calculate the vector spin chirality for $S=1/2$ zigzag spin chains having U(1) symmetry, using the density matrix renormalization group combined with unitary transformation. We then demonstrate the occurrence of the chiral order for the zigzag XY chain and discuss the associated phase transition. The results are consistent with the analysis based on the bosonization and the long distance behaviour of the chirality correlation function. For the $S=1/2$ zigzag Heisenberg chain in a magnetic field, we also verify the chiral order that is predicted by the effective field theory and the chirality correlation function, and then determine its magnetic phase diagram.Comment: 7 pages, 9 figures, accepted for publication in J. Phys. Soc. Jp

Kramers-Wannier Approximation for 3D Ising Model

We investigate the Kramers-Wannier approximation for the three-dimensional (3D) Ising model. The variational state is represented by an effective 2D Ising model, which contains two variational parameters. We numerically calculate the variational partition function using the corner transfer matrix renormalization group (CTMRG) method, and find its maximum with respect to the variational parameters. The calculated transition point $K_{\rm c} = 0.2184$ is only 1.5% less than the true $K_{\rm c}$; the result is better than that obtained by the corner transfer tensor renormalization group (CTTRG) approach. The calculated phase transition is mean-field like.Comment: 7 pages, 4 figures, submitted to Prog. Theor. Phy

Anomalous magnetization process in frustrated spin ladders

We study, at T=0, the anomalies in the magnetization curve of the S=1 two-leg ladder with frustrated interactions. We focus mainly on the existence of the M=\Ms/2 plateau, where \Ms is the saturation magnetization. We use analytical methods (degenerate perturbation theory and non-Abelian bosonization) as well as numerical methods (level spectroscopy and density matrix renormalization group), which lead to the consistent conclusion with each other. We also touch on the M=\Ms/4 and M=(3/4)\Ms plateaux and cusps.Comment: 4 pages, 7 figures (embedded), Conference paper (Highly Frustrated Magnetism 2003, 26-30th August 2003, Grenoble, France

Wilson-like real-space renormalization group and low-energy effective spectrum of the XXZ chain in the critical regime

We present a novel real-space renormalization group(RG) for the one-dimensional XXZ model in the critical regime, reconsidering the role of the cut-off parameter in Wilson's RG for the Kondo impurity problem. We then demonstrate the RG calculation for the XXZ chain with the free boundary. Comparing the hierarchical structure of the obtained low-energy spectrum with the Bethe ansatz result, we find that the proper scaling dimension is reproduced as a fixed point of the RG transformation.Comment: 4 pages, 6 figures, typos corrected, final versio

Self-Consistent Tensor Product Variational Approximation for 3D Classical Models

We propose a numerical variational method for three-dimensional (3D) classical lattice models. We construct the variational state as a product of local tensors, and improve it by use of the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG) applied to 2D classical systems. Numerical efficiency of this approximation is investigated through trial applications to the 3D Ising model and the 3D 3-state Potts model.Comment: 12 pages, 6 figure